Imaging devices, such as digital still cameras, camera phones (“camphones”), video recorders, digital scanners, and digital copiers, use photodetector arrays to produce electronic signals that are capable of producing images output to a display or printer. A typical photodetector array has many individual photosites or picture elements (“pixels”), each of which is responsive over a relatively wide range of wavelengths. The magnitude of the electrical signal produced by a single photodetector at different wavelengths of light varies according to the wavelength response of the photodetector. To form a color image, color pass filters are typically placed over individual photodetectors so that each photodetector is responsive to a relatively narrow wavelength range of light.
The photosites in a photodetector array are often called “pixels” because each photodetector generates an electronic signal typically used to produce a picture cell in an image. The pixels in a photodetector array are typically spaced in a repeating fashion, and pixel spacing is often referred to in terms of pitch, which is the center-to-center spacing between pixels in a photodetector array. In color photodetector arrays, the pitch is often different for pixels responsive to the different colors.
The image captured by the image sensor is sampled by the photodetector array, that is, a continuous image is reconstructed from the data detected by the individual pixels. The more closely spaced the pixels are, the higher the sampling frequency, and the more data there is to reconstruct the image from. It is generally desirable that the reconstructed image is a faithful reproduction of the original image. However, an image that contains input (such as closely spaced lines) at a higher frequency than twice the sampling frequency may cause the resultant image to not be a faithful reproduction of the original image.
As long as the sampling frequency is more than twice as high as the highest frequency in the signal (image), the sampled image will be a proper representation of the original image. If, however, the sampling frequency is less than twice as high as the highest frequency to be sampled, the sampled image will contain extraneous components called “aliases.” The generation of aliases is called aliasing. Aliasing is avoided in digital imaging systems by providing a low pass filter to eliminate frequency components higher than one-half the sampling frequency (also known as the “Nyquist frequency”) from reaching the photodetector array.
A more detailed discussion of aliasing, including figures illustrating aliasing effects is provided in the paper entitled “Color dependent optical prefilter for the suppression of aliasing artifacts,” by John E. Greivenkamp, published in APPLIED OPTICS, Vol. 29, No. 5, 676–84 (Feb. 10, 1990).
FIG. 1A illustrates an aliasing effect. An original image 10 includes alternating dark 11, 13 and light 12, 18, 24 lines. The spacing of the lines is the “image frequency.” A photodetector array 14 includes a plurality of photosites (pixels) 15, 16, 17 that are not as closely spaced as the closely spaced lines imaged onto the photodetector array. The first pixel 15 is mostly illuminated with a dark line 11, thus producing a dark output 20. The second pixel 16 is partially illuminated with a dark line 13 and partially illuminated with a white line 18, thus producing a medium (gray) output 22, and the third pixel 17 is mostly illuminated with a white line 24, thus producing a light output 26. Note that the output from the pixels produces a different pattern and lower frequency than the original image. Anti-aliasing filters (also known as “blur filters”) are used to reduce the effects of aliasing, at the expense of reduced image sharpness.
Conventional blur filters are made of a birefringent crystal, such as quartz crystal or lithium niobate, cut at a particular crystalline orientation (typically 45 degrees with respect to the crystal lattice orientation) to a specific thickness. Such filters are known as double-refraction or “Savart” plates. A double-refraction plate (“DRP”) separates an incoming ray of light into an “ordinary ray” and an “extraordinary ray” having different polarization states.
FIG. 1B shows a DRP 40 separating an incoming ray of light (“ray”) 42 into an ordinary ray 44 and an extraordinary ray 46. The distance “d” between the ordinary ray 44 and extraordinary ray 46 depends on the thickness “t” of the DRP 40 and the difference between the ordinary and extraordinary indices of refraction of the DRP 40. Double ended arrows 37, 39 indicate that the ordinary ray 44 has a different polarization state 37 than the polarization state 39 of the extraordinary ray 46. A typical thickness for a quartz DRP to be used with a 5 mega-pixel photodetector array having a pixel pitch of 2.8 microns is about 0.3 mm.
In color imaging systems, a retarder plate (¼ wave plate) and a second DRP are sometimes used to provide two-dimensional blurring. A typical thickness for such an assembly is about 1.2 mm. Thus, using quartz DRPs results in a relatively thick, heavy assembly, which is generally undesirable and particularly undesirable for compact, portable imaging devices such as digital still cameras, video cameras, and camphones. Furthermore, quartz DRPs are relatively expensive components.
Therefore, it is desirable to provide aliasing filters that avoid the disadvantages of the prior art.